广义特殊Tzitzeica-Dodd-Bullough类型方程的行波解(英文)

本文研究了广义特殊Tzitzeica-Dodd-Bullough类型方程,利用动力系统分支理论方法,证明该方程存在周期行波解,无界行波解和破切波解,并求出了一些用参数表示的显示精确行波解.

Tzitzéica方程的Bcklund变换和显式精确解

Bcklund变换是求解非线性偏微分方程的一种有效方法,文章应用扩展的齐次平衡法得到了Tzitzéica方程u xt=peu-qe-2u的一种Bcklund变换和精确解,尤其得到了Tzitzéica方程,Dodd-Bullough-Mikhailov方程和Tzitzéica-Dodd-Bullough方程的精确解.

Bright and dark soliton solutions for some nonlinear fractional differential equations

In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.

Coiflet solution of strongly nonlinear p-Laplacian equations

A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the coefficients are used as the single-point samplings. The obtained approximation formula can exactly represent any polynomials defined on the interval with the order up to one third of the length of the compact support of the adopted Coiflet function. Based on the Galerkin method, a Coifiet-based solution procedure is established for general two-dimensional p^Laplacian equations, following which the equations can be discretized into a concise matrix form. As examples of applications, the proposed modified wavelet Galerkin method is applied to three typical p-Laplacian equations with strong nonlinearity. The numerical results justify the efficiency and accuracy of the method.

MEROMORPHIC SOLUTIONS OF SOME TYPES OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS

Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we ob- tain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.

Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility

The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The （2＋1）-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.

New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota-Satsuma KdV System

In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.

Compact implicit integration factor methods for some complex-valued nonlinear equations

The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.

THE ASSOCIATED FAMILIES OF SEMI-HOMOGENEOUS COMPLETE HYPERBOLIC AFFINE SPHERES

Hildebrand classified all semi-homogeneous cones in R3 and computed their cor- responding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand＇s new examples. After giving their affine metrics and affine cubic forms, we construct the whole associated family for each of Hildebrand＇s examples. The generic member of these affine spheres is given by Weierstrass f,ζ and a functions. In general any regular convex cone in R^3 has a natural associated S^1-family of such cones, which deserves further studies.

A GENERALIZED GAUSS-TYPE QUADRATURE FORMULA AND ITS APPLICATIONS TO PSEUDOSPECTRAL METHOD

A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.

Review on Modeling and Optimization for Refractories

This paper introduced characteristics of refractories and step of simulation. During simulation,firstly analyzed mechanism of technology; secondly described the mechanism as quadratic equation; thirdly designed and executed experiment; later made regression equation and optimization; then found technical conflict; finally analyzed and resolved the conflict. Doing repeatedly like this,resolved difficult problems.

Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays

By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows . Some new results for existence of T-periodic solutions to such equations are obtained.

Electromagnetic Scattering in a Two-layered Medium

The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.

Investigation on the Natural Modes of A Semi-Closed Floating Tank

Vessels with semi-closed tanks(i.e.,well docks)are widely applied in the military operation and maritime engineer-ing.The water is bound by the semi-closed floating tank and forced by both the incident waves and ship’s motions.The free surface oscillations inside the flooded well dock is thus distinctive and very complicated.So far,the natural modes of semi-closed floating tanks have not yet been studied.This paper investigates the characteristics of natural modes of a floating semi-closed tank by combining a mode-resolving model based on mild-slope equations and a hydrodynamic model based on computational fluid dynamics.Results show that the first three natural periods(i.e.,74,23.6,and 14 s)of the tank fall into the band of swell and infragravity waves and they could be triggered under certain circumstance.Multi-period free surface oscillations are observed inside the tank,including the longest natural period(i.e.,74 s),though the incident waves are monochromatic.A possible generation mechanism for the long-period mode is explained on the basis of liquid sloshing and harbor oscillations.Moreover,a long-period component with a period close to the natural mode of well dock is observed in the ship motions,which is generated by the interaction between the waves and ship.

Optimization of multibody systems based on the generalized-α projection method for DAEs

Efficient optimization strategy of multibody systems is developed in this paper. Aug- mented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on second order sensitivity are used to solve the unconstrained problem, where the sensitivity is solved by hybrid method. Generalized-α method and generalized-α projection method for the differential-algebraic equation, which shows more efficient properties with the lager time step, are presented to get state variables and adjoint variables during the optimization procedure. Numerical results validate the accuracy and efficiency of the methods is presented.

Solutions of Zhiber-Shabat and Related Equations Using a Modified tanh-coth Function Method

The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions and rational functions. The modified tanh-coth function method is easy to execute, brief, efficient, and can be used to solve many other nonlinear evolution equations.

Double Exp-Function Method for Multisoliton Solutions of The Tzitzeica-Dodd-Bullough Equation

In this work, it is aimed to find one- and two-soliton solutions to nonlinear Tzitzeica-Dodd-Bullough （TDB） equation. Since the double exp-function method has been widely used to solve several nonlinear evolution equations in mathematical physics, we have also used it with the help of symbolic computation for solving the present equation. The method seems to be easier and more accurate thanks to the recent developments in the field of symbolic computation.

Well-Posedness of Stochastic Continuity Equations on Riemannian Manifolds

The authors analyze continuity equations with Stratonovich stochasticity,■ρ+divh[ρo(u(t,x)+∑_(i=1)^(N)a_(i)(x)w_(i)(t))]=0defined on a smooth closed Riemannian manifold M with metric h.The velocity field u is perturbed by Gaussian noise terms Wi(t),:WN(t)driven by smooth spatially dependent vector fields a1(x),...,aN(x)on M.The velocity u belongs to L_(t)^(1)W_(x)^(1,2)with divh u bounded in Lf,for p>d+2,where d is the dimension of M(they do not assume div_(h) u∈L_(t,x)^(∞)).For carefully chosen noise vector fields ai(and the number N of them),they show that the initial-value problem is well-posed in the class of weak L^(2) solutions,although the problem can be ill-posed in the deterministic case because of concentration effects.The proof of this“regularization by noise”result is based on a L^(2) estimate,which is obtained by a duality method,and a weak compactness argument.

High-order accurate dissipative weighted compact nonlinear schemes

Based on the method deriving dissipative compact linear schemes ( DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis, the dissipative and dispersive features of DWCNS are discussed. In view of the modified wave number, the DWCNS are equivalent to the fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the accuracy of DWCNS. Boundary and near boundary schemes are developed and the asymptotic stabilities of DWCNS on both uniform and stretching grids are analyzed. The multi-dimensional implementations for Euler and Navier-Stokes equations are discussed. Several numerical inviscid and viscous results are given which show the good performances of the DWCNS for discontinuities capturing, high accuracy for boundary layer resolutions, good convergent rates (the root-mean-square of residuals approaching machine zero for solutions with strong shocks) and especially the damping effect on the spurious oscillations which were found in the solutions obtained by TVD and ENO schemes.

Wolbachia infection dynamics by reaction-diffusion equations

Dengue fever is caused by the dengue virus and transmitted by Aedes mosquitoes.A promising avenue for eradicating the disease is to infect the wild aedes population with the bacterium Wolbachia driven by cytoplasmic incompatibility(CI).When releasing Wolbachia infected mosquitoes for population replacement,it is essential to not ignore the spatial inhomogeneity of wild mosquito distribution.In this paper,we develop a model of reaction-diffusion system to investigate the infection dynamics in natural areas,under the assumptions supported by recent experiments such as perfect maternal transmission and complete CI.We prove non-existence of inhomogeneous steady-states when one of the diffusion coefficients is sufficiently large,and classify local stability for constant steady states.It is seen that diffusion does not change the criteria for the local stabilities.Our major concern is to determine the minimum infection frequency above which Wolbachia can spread into the whole population of mosquitoes.We find that diffusion drives the minimum frequency slightly higher in general.However,the minimum remains zero when Wolbachia infection brings overwhelming fitness benefit.In the special case when the infection does not alter the longevity of mosquitoes but reduces the birth rate by half,diffusion has no impact on the minimum frequency.